Can there be “groups within groups”?

Hello, love Buddypress so far, thanks for everything you guys do. Sorry if this is a newbie question…

I’m building a Buddypress site for a company that puts on sports tournaments. I’ve already got Buddypress installed and running. I’ve created groups for each tournament, so players who are participating can “join” their tournament and talk about it with each other.

THE THING IS, these are TEAM tournaments, not simply individual players. I also want these players to be able to “join” their TEAMS. So each tournament has several teams, each team has several players. See what I mean?

How do I go about creating groups for this type of organizational model? A “group within a group” (teams within tournaments). Can you please walk me through this process once, so I can play with it from there?